# Changeset 2834:4eed73fe6f31

Ignore:
Timestamp:
02/07/07 20:48:06 (6 years ago)
Branch:
default
Message:

add examples.

File:
1 edited

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• ## sage/schemes/elliptic_curves/ell_rational_field.py

 r2822 misc.verbose("index = %s"%ind) # Compute upper bound on square root of index. if ind.length() < 1: if ind.absolute_diameter() < 1: t, i = ind.is_int() if t:   # unique integer in interval, so we've found exact index squared. ignore_nonsurj_hypothesis=False): """ Given a fundamental discriminant D (=-3,-4) that satisfies the Given a fundamental discriminant D (!= -3,-4) that satisfies the Heegner hypothesis, return a list of primes so that Kolyvagin's theorem (as in Gross's paper) implies that any correct up to addition or a real number with absolute value less than \$10^{-10}\$. EXAMPLES: sage: E = EllipticCurve('37a') sage: E.shabound_kolyvagin() ([2], 1) sage: E = EllipticCurve('141a') sage: E.sha_an() 1 sage: E.shabound_kolyvagin() ([2, 7], 49) We get no information the curve has rank \$2\$. sage: E = EllipticCurve('389a') sage: E.shabound_kolyvagin() (0, 0) sage: E = EllipticCurve('681b') sage: E.sha_an() 9 sage: E.shabound_kolyvagin() ([2, 3], 9) """ if self.has_cm(): if t: break elif I.length() < 1: elif I.absolute_diameter() < 1: raise RuntimeError, "Problem in shabound_kolyvagin; square of index is not an integer -- D=%s, I=%s."%(D,I) misc.verbose("Doubling bounds")
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